What Is The Unknown In The Problem?The Total Number Of Questions On The Survey, T T T .Given: 16 T = 80 % \frac{16}{t}=80 \% T 16 = 80% Write The Percent As A Rate Per 100: 16 T = □ 100 \frac{16}{t}=\frac{\square}{100} T 16 = 100 □

Mar 9, 2025 by ADMIN 238 views

**What is the Unknown in the Problem?**

In mathematics, problems often involve unknown quantities that need to be determined. Identifying the unknown in a problem is a crucial step in solving it. In this article, we will explore how to identify the unknown in a problem and use it to solve an equation.

Understanding the Problem

The problem states that the total number of questions on a survey is represented by the variable $t$ . We are given an equation that relates the number of questions to a percentage: $\frac{16}{t}=80 \%$ . Our goal is to write the percent as a rate per 100.

Rewriting the Percent as a Rate per 100

To rewrite the percent as a rate per 100, we need to convert the percentage to a decimal. We can do this by dividing the percentage by 100. In this case, we have $80 \% = \frac{80}{100}$ . We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20. This gives us $\frac{80}{100} = \frac{4}{5}$ .

Writing the Percent as a Rate per 100

Now that we have the percent as a decimal, we can rewrite the equation as a rate per 100. We can do this by multiplying both sides of the equation by 100. This gives us $\frac{16}{t} \times 100 = \frac{4}{5} \times 100$ . Simplifying this equation, we get $\frac{1600}{t} = 80$ .

Solving for the Unknown

Now that we have the equation in the form $\frac{1600}{t} = 80$ , we can solve for the unknown variable $t$ . To do this, we can multiply both sides of the equation by $t$ to get rid of the fraction. This gives us $1600 = 80t$ . Next, we can divide both sides of the equation by 80 to solve for $t$ . This gives us $t = \frac{1600}{80}$ .

Simplifying the Solution

To simplify the solution, we can divide both the numerator and the denominator by their greatest common divisor, which is 80. This gives us $t = \frac{20}{1}$ .

Conclusion

In this article, we identified the unknown in a problem and used it to solve an equation. We started by rewriting the percent as a rate per 100 and then solved for the unknown variable $t$ . The final solution was $t = 20$ . This example illustrates the importance of identifying the unknown in a problem and using it to solve equations.

Discussion

The problem presented in this article is a classic example of a proportion problem. Proportion problems involve setting up a ratio between two quantities and then solving for the unknown quantity. In this case, we set up a ratio between the number of questions and the percentage, and then solved for the unknown variable $t$ .

Real-World Applications

Proportion problems have many real-world applications. For example, in business, proportions are used to calculate profit margins, interest rates, and other financial metrics. In science, proportions are used to calculate the concentration of a solution, the density of a material, and other physical properties.

Tips for Solving Proportion Problems

When solving proportion problems, it's essential to identify the unknown quantity and set up a ratio between the two quantities. Then, use algebraic techniques to solve for the unknown quantity. Here are some tips for solving proportion problems:

Identify the unknown quantity and set up a ratio between the two quantities.
Use algebraic techniques to solve for the unknown quantity.
Check your solution by plugging it back into the original equation.
Use proportions to solve real-world problems, such as calculating profit margins, interest rates, and other financial metrics.

Conclusion

In our previous article, we explored how to identify the unknown in a problem and use it to solve an equation. In this article, we will answer some frequently asked questions about identifying the unknown in a problem.

Q: What is the unknown in a problem?

A: The unknown in a problem is the quantity that we are trying to find or determine. It is the variable or value that we are solving for.

Q: How do I identify the unknown in a problem?

A: To identify the unknown in a problem, you need to read the problem carefully and look for the variable or value that is being asked to be found. You can also look for words or phrases such as "find," "determine," or "solve for."

Q: What are some common types of unknowns in problems?

A: Some common types of unknowns in problems include:

Variables: These are letters or symbols that represent unknown values.
Constants: These are numbers that do not change value.
Expressions: These are combinations of variables and constants that are used to represent unknown values.

Q: How do I write the percent as a rate per 100?

A: To write the percent as a rate per 100, you need to divide the percentage by 100. For example, if you have 80%, you can write it as 80/100.

Q: What is the difference between a proportion and an equation?

A: A proportion is a statement that two ratios are equal, while an equation is a statement that two expressions are equal. For example, the statement "2/3 = 4/6" is a proportion, while the statement "2x + 3 = 5" is an equation.

Q: How do I solve a proportion problem?

A: To solve a proportion problem, you need to set up a ratio between the two quantities and then solve for the unknown quantity. You can use algebraic techniques, such as cross-multiplication, to solve for the unknown quantity.

Q: What are some real-world applications of proportion problems?

A: Proportion problems have many real-world applications, including:

Business: Proportions are used to calculate profit margins, interest rates, and other financial metrics.
Science: Proportions are used to calculate the concentration of a solution, the density of a material, and other physical properties.
Engineering: Proportions are used to design and build structures, such as bridges and buildings.

Q: What are some tips for solving proportion problems?

A: Here are some tips for solving proportion problems:

Identify the unknown quantity and set up a ratio between the two quantities.
Use algebraic techniques, such as cross-multiplication, to solve for the unknown quantity.
Check your solution by plugging it back into the original equation.
Use proportions to solve real-world problems, such as calculating profit margins, interest rates, and other financial metrics.

Conclusion

In conclusion, identifying the unknown in a problem is a crucial step in solving it. By understanding the different types of unknowns, writing the percent as a rate per 100, and solving proportion problems, we can solve a wide range of problems. We hope that this Q&A article has been helpful in answering your questions about identifying the unknown in a problem.